BAYESIAN-ESTIMATION OF NMR SPECTRAL PARAMETERS UNDER LOW SIGNAL-TO-NOISE CONDITIONS

The Bayesian statistical method of spectral estimation is applied to N MR free induction decay signals at various values of signal-to-noise r atio (SNR). The frequency and amplitude estimates from the Bayesian ca lculations are more accurate than those from the commonly used fast Fo urier transformation (FFT) of the same data sets. Both real and synthe tic data sets are examined with the Bayesian results being superior in all cases. In addition to the superior performance at low SNR the Bay esian derived amplitudes and frequency estimates were not as affected by signal decay as in Fourier Transformed spectra. Finally, the amplit udes obtained are equal to the FFT integrated intensities resulting in an apparent frequency domain signal-to-noise ratio (SNR) greater than the FFT SNR by a factor proportional to the FFT frequency domain line width. For typical high resolution spectra this improvement was approx imately a factor of 2.5. Even greater improvement is obtained when rap idly decaying signals art analyzed. Bayesian computation time for the 6 line p-chloroanaline and chloroform spectrum was approximately 12 mi nutes on a modem computer work station.